# What is the equation of the line normal to # f(x)=sqrt(1/(x^2+2) # at # x=1#?

##### 1 Answer

#### Explanation:

in simplifying the equation we get

We then apply the chain rule to get

Then we substitute in 1 for x to find the gradient of the tangent at x=1

This results us getting

Now we know the gradient, we just need the co-ordinates which it runs through. We then sub x=1 back int the original equation to find the point which the normal will pass through. The y value, after subsitution is

Therefore by substituting the numbers/values into the point gradient formula, we'll find the equation of the normal. The point gradient formula is